Beyond the outlined structural similarities between Pavlov's and Hebb's representations of learning, the intrinsically dynamical process underlying Pavlovian association mechanism highglights a phenomenon that can not be captured by the statistical mechanical approach underlying Hebbian storage [1]}, [2]}: if the network gets stuck in retrieving persistently the same pattern (i.e., an obsession), each retrieval reinforces always the same minimum in the memory landscape up to the point that the latter destroyes all the other memories and solely the obsessive pattern remains stored. In Fig. REF  we report results of the following numerical experiment that confirms such a scenario: starting from a perfect Hebbian kernel \(J^{(Hebb)}\) , we let the nework retrieve always the first pattern (i.e., the field is persistently \(h=\xi ^1\) ) and we evaluate, iteratively in \(n\) , the evolution both of \(||J^{(n)}-J^{(Hebb)}||_{F}\)  and \(||J^{(n)}-J^{(\mu =1)}||_{F}\) , where \(J^{(\mu =1)}=\xi _i^1\xi _j^1\) . Remarkably, in the long time limit, the synaptic matrix collapses onto \(\xi ^1\)  (i.e. \(\lim _{n \rightarrow \infty } J^{(n)} = J^{(\mu =1)}\) ), while \(||J^{(n)}-J^{(Hebb)}||_F \rightarrow \sqrt{1-\frac{1}{K}}\)  as expected.
